Question

The sides of a triangle are 60, 68, and 32. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

Answer 1

To determine whether the triangle is right, acute, or obtuse, we need to check if it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

We can start by finding the longest side, which is 68. Then, we can check whether it satisfies the Pythagorean Theorem using the other two sides:

68^2 = 4624
60^2 + 32^2 = 3600 + 1024 = 4624

Since 68^2 = 60^2 + 32^2, the triangle satisfies the Pythagorean Theorem and is therefore a right triangle